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1 year ago in Computational Physics , Optics By Mukesh

What is the maximum number of Zernike polynomials that can be fitted before numerical instability occurs?

We use these fits for high-precision tasks like designing adaptive optics systems and characterizing human eyes. While theory suggests an infinite basis, our sensor data is noisy and discrete. Pushing for higher-order correction seems beneficial, but we've all seen reconstructions become wildly oscillatory and non-physical. I'm looking for a rule-of-thumb grounded in numerical analysis or specific experimental studies.

WavePropagation ZernikePolynomials

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By Preetham M Answered 1 year ago

Based on my experience in adaptive optics, I would recommend a pragmatic approach. The limit isn't a fixed number but a function of your data's spatial sampling and signal-to-noise ratio. For well-sampled, high-quality wavefronts from a Shack-Hartmann sensor, I've seen stable reconstructions up to ~10th radial order (which is about 65 terms). Beyond that, the condition number of the fitting matrix explodes, and you're fitting noise. I always advocate for cross-validation: if adding a higher order doesn't improve prediction on a withheld data subset, you've hit your practical limit.

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What is the maximum number of Zernike polynomials that can be fitted before numerical instability occurs?

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